A simple propositional calculus for compact Hausdor spaces (original) (raw)

We introduce a simple propositional calculus for compact Hausdor spaces. Our approach is based on de Vries duality. The main new connective of our calculus is that of strict implication. We de ne the strict implication calculus SIC as our base calculus. We show that the corresponding variety SIA of strict implication algebras is a discriminator and locally nite variety. We prove that SIC is strongly sound and complete with respect to the universal subclass RSub of SIA, where the modality associated with the strict implication only takes on the values of 0 and 1. We develop Π2-rules for strict implication algebras, and show that every Π2-rule de nes an inductive subclass of RSub. We prove that every derivation system axiomatized by Π2-rules is strongly sound and complete with respect to the inductive subclass of RSub it de nes. We introduce the de Vries calculus DVC and show that it is strongly sound and complete with respect to the class of compingent algebras, and then use MacNeill...